6 Z 2 × Z 2 - symmetric spaces
نویسندگان
چکیده
The notion of a Γ-symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group Γ replaces the group Z 2. The case Γ = Z k has also been studied, from the algebraic point of view by V.Kac [10] and from the point of view of the differential geometry by Ledger, Obata [12], Kowalski [11] or Wolf-Gray [18] in terms of k-symmetric spaces. In this case, a k-manifold is an homogeneous reductive space and the classification of these varieties is given by the corresponding classification of graded Lie algebras. The general notion of a Γ-symmetric space was introduced by R.Lutz in [14]. We approach the classification of such spaces in the case Γ = Z 2 × Z 2 using recent results (see [3]) on the classification of comp[lex Z 2 × Z 2-graded simple Lie algebras.
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